In this paper, we propose a generic algorithmic framework which defines a unified view of fractal decomposition algorithms for continuous optimization. Fractals allow building a hierarchical decomposition of the decision space by using a self-similar geometrical object. The proposed generic framework is made of five distinct and independent search components: fractal geometrical object, tree search, scoring, exploration and exploitation. The genericity of the framework allowed the instantiation of popular algorithms from the optimization, machine learning and computational intelligence communities. Moreover, new optimization algorithms can be designed using various strategies of the search components. This shows the modularity of the proposed algorithmic framework. The computational experiments emphasize the behaviors of fractal-based approaches in terms of scalability, robustness, and the balance between exploitation and exploration in the search space. The obtained results show the significance of each search component of the fractal framework, and the necessity to build harder and well-defined benchmarks which can assess the performance of deterministic, axis-aligned and symmetrical decomposition-based algorithms.